is 4d exist? could u tell me proof
Answers
Answer:
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring its length, width, and height (often labeled x, y, and z).
Single locations in 4D space can be given as vectors or n-tuples, i.e. as ordered lists of numbers such as (t,x,y,z). It is only when such locations are linked together into more complicated shapes that the full richness and geometric complexity of 4D and higher dimensional spaces emerge. A hint to that complexity can be seen in the accompanying animation of one of the simplest possible 4D objects, the 4D cube or tesseract.
The number of dissmisive replies here is shocking so let me give a contructive answer. It all really comes down to us insisting that in our space(time), whatever it be, the “length” of a position vector is the same in all reference frames.
In 3D Euclidian space, a position vector is fully characterized by three numbers x,y,z which we call the Cartesian coordinates and the length-squared of such a vector is x²+y²+z² and you can verify that if you rotate or move your coordinate system, this length will always be the same. The distance between your home and workplace doesn’t change whether you look from ground or in bird’s eye view!
Now in Special relativity, every event is fully characterized by four unique numbers - x,y,z, and ct. All events can be discribed by these four coordinates and no less hence they form a basis of the space of events - you spill your coffee on (5th avenue, 21st street, 4th floor, 8am). It turns out that the only way to define “length” so that it would be invariant is of the form s²=x²+y²+z²−(ct)². This new “length” is the same as seen by people in fast rockets, spinning or standing still just like your home-workplace distance from ground and bird’s eye! And is the “normal” spacial length x²+y²+z² still invariant? No longer - objects might appear to have different sizes to different observers. It’s counterintuitive but inevitable!
So yes, the temporal dimension is distinct and fundamentally different from the three spacial, as indicated by the minus sign, but time is the 4th dimension because without it we cannot construct any meaningful position vector with invariant length.
Answer:
no 4 d don't exist there is 2d and 3d only